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People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below.

Pink lemonade: 156 males, 72 females
Yellow lemonade: 104 males, 48 females

The events "prefers pink lemonade” and "female” are independent because

P(pink lemonade | female) = P(pink lemonade) = 0.6.
P(female | pink lemonade ) = P(pink lemonade) = 0.3.
P(pink lemonade | female) = 0.3 and P(pink lemonade) = 0.6.
P(female | pink lemonade ) = 0.3 and P(pink lemonade) = 0.6.

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Answered by GPT-5 mini AI
Answer: "P(pink lemonade | female) = P(pink lemonade) = 0.6."

Calculation: total = 156+72+104+48 = 380. P(pink) = 228/380 = 0.6. P(pink | female) = 72/120 = 0.6. Since P(pink|female) = P(pink), the events are independent.